Evaluating Strategic Workforce Decisions in Aggregate Production Planning under Demand Uncertainty: A Two-Stage Stochastic MILP with Out-of-Sample Assessment

Öz

Aggregate production planning (APP) requires balancing workforce and operational decisions over a medium-term horizon. This study formulates and applies a two-stage stochastic mixed integer linear program (MILP) for APP with the primary objective of evaluating strategic workforce planning decisions under demand uncertainty. Workforce decisions are modeled as here-and-now commitments, while operational decisions are optimized as recourse actions in response to realized demand. The framework is demonstrated in an illustrative furniture manufacturing setting over a 12-month horizon with seasonally varying cost parameters. Demand scenarios are generated by combining Holt–Winters point forecasts with forecast-error scenarios obtained through a rolling-origin procedure and a moment-matching approach, yielding demand trajectories that reflect the statistical properties and temporal dependence of forecast uncertainty. Using these scenarios, the model quantifies cost–service trade-offs under alternative backorder penalty severities. To assess the robustness of the resulting workforce plans, this study conducts an out-of-sample evaluation based on observed demand from a holdout year and a wait-and-see benchmark, a validation perspective that has received limited attention in the APP literature. The out-of-sample results indicate that the stochastic model produces feasible and cost-effective workforce decisions that remain near-optimal under observed demand. Overall, the proposed framework serves as an effective decision-support tool for APP under demand uncertainty, supporting the evaluation of workforce and operational decisions within a unified stochastic framework.

Anahtar Kelimeler

• Aggregate production planning
• Two-stage stochastic programming
• Demand uncertainty
• Scenario generation
• Moment matching scenario generation
• Out-of-sample evaluation

Talep Belirsizliği Altında Toplam Üretim Planlamasında Stratejik İşgücü Planlamasının Değerlendirilmesi: İki Aşamalı Stokastik MILP Yaklaşımı ve Örneklem Dışı Analizi

Öz

Toplam üretim planlaması, orta vadeli bir planlama ufkunda işgücü ve operasyonel kararlar arasında denge kurulmasını gerektirir. Bu çalışma, talep belirsizliği altında stratejik işgücü planlama kararlarını değerlendirmeyi amaçlayan iki aşamalı stokastik bir karma tamsayılı doğrusal programlama modeli geliştirmekte ve uygulamaktadır. İşgücü kararları, talep gerçekleşmeden önce verilen burada-ve-şimdi (here-and-now) kararlar olarak modellenirken, operasyonel kararlar gerçekleşen talebe bağlı olarak telafi (recourse) kararları şeklinde optimize edilmektedir. Önerilen çerçeve, mevsimsellik içeren maliyet yapısına sahip 12 aylık bir planlama ufku altında, örnek bir mobilya üretim uygulaması üzerinden gösterilmektedir.
Talep senaryoları, Holt–Winters nokta tahminleri ile kayan başlangıçlı (rolling-origin) bir prosedür ve moment eşleştirme yaklaşımı kullanılarak elde edilen tahmin hatası senaryolarının birleştirilmesiyle oluşturulmakta; böylece talep belirsizliğinin istatistiksel özelliklerini ve zamansal bağımlılığını yansıtan talep yörüngeleri elde edilmektedir. Bu senaryolar kullanılarak, farklı geri sipariş ceza şiddeti varsayımları altında maliyet–hizmet düzeyleri arasındaki ödünleşimler nicel olarak analiz edilmektedir. Elde edilen işgücü planlarını değerlendirmek amacıyla, bu çalışma ayrıca model kurulumunda kullanılmayan bir tutma yılına (holdout year) ait gözlemlenen talep verilerine dayalı bir örneklem dışı değerlendirme ve bekle-ve-gör (wait-and-see) kıyaslaması gerçekleştirmektedir. Toplam üretim planlama literatüründe sınırlı ölçüde ele alınan bu doğrulama yaklaşımı, stokastik planlamanın pratik performansına ilişkin nicel analizler sunmaktadır. Örneklem dışı sonuçlar, stokastik modelden elde edilen işgücü kararlarının gözlemlenen talep altında da uygulanabilir ve maliyet açısından etkin olduğunu, ayrıca mükemmel bilgi varsayımı altındaki çözümlere yakın performans sergilediğini göstermektedir. Genel olarak, önerilen çerçeve talep belirsizliği altında toplam üretim planlaması için etkili bir karar destek aracı sunmakta ve işgücü ile operasyonel kararların bütünleşik bir stokastik yapı içinde değerlendirilmesine olanak sağlamaktadır.

Anahtar Kelimeler

• Toplam üretim planlaması
• İki aşamalı stokastik programlama
• Talep belirsizliği
• Moment eşleştirme tabanlı senaryo üretimi
• Örneklem dışı değerlendirme

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